I've seen my daughter rename her Instagram name several times.
https://help.instagram.com/116836975134193/
How do I update my profile information (ex: name, username, email)?
To update your profile information:
1. Go to your profile by tapping
2. Tap Edit Your Profile
3. Type in your new name, username, website or bio and then tap Done (iPhone), Save (Android) or the check mark (Windows Phone)